Estimation and control in the wet end using CO2

ABSTRACT

A method for controlling the CO 2  addition in a wet end process utilizing CO 2  addition is disclosed. The method includes combining a papermaking composition and CO 2  to create a CO 2 -enriched papermaking composition, measuring or estimating at least one electrical property of either the papermaking composition or of the CO 2 -enriched papermaking composition, and controlling the rate of addition of CO 2  to maintain the at least one electrical property within a pre-selected range of values.

CROSS REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of U.S. ProvisionalApplication No. 60/479,285, filed Jun. 18, 2003 and U.S. ProvisionalApplication No. 60/479,284, filed Jun. 18, 2003.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The disclosure relates to a method for controlling the CO₂addition in a wet end process utilizing CO₂ addition.

[0004] 2. Related Art

[0005] A method for controlling the CO₂ addition in a wet end processutilizing CO₂ addition is disclosed. The assignee of this application,Air Liquide, currently has pending a patent application for CO₂ additionin a wet end process.

[0006] In paper processing, due to industrial competition, changes inraw materials, environmental concerns and greater customer demands,higher levels of knowledge and understanding of the chemistry in the wetend are important to commercial success. It has been discovered that thezeta potential (ZP) is an important property in the final paper qualityfabrication.

[0007] It has long been understood that zeta potential plays animportant role in paper machine process operability by being related toflocculation, retention and drainage characteristics of the pulp. N.Vanderhoek, “Optimizing Paper Machine Performance Through ElectrokineticMeasurement”, APPITA, Vol. 47. No. 5, pp 397-405, 1994. Wet-endstability is a key part to getting machine efficiencies. T. Miyanashi,et. al. studied the effects of zeta potential on these phenomena, andconcluded that the zeta potential should be controlled to provide betterflocculation and drainage additives. The wet end chemistry of optimizedpaper machines is not operated at equilibrium conditions, and the orderof chemical addition is critical. T. Miyanashi, and S. Motegi,“Optimizing Flocculation and Drainage for Microparticle by ControllingZeta Potential,” TAPPI Journal, pp. 262-270, January 1997.

[0008] The need for better performance of paper machines has triggeredthe development of better retention aids. This has defined a need forbetter understanding the effects of these new, wet-end additives andbeing able to control in real time the additions to obtain optimum papermachine and overall wet-end operation performances. The first step toachieving these objectives relies on available real-time information. Itis desirable to provide a process that adapts itself to real timechanges. In the wet-end process, fiber characteristics, chemicaladditives and water properties can change continuously, and so it isdesired to detect these variations as they occur in real time.

[0009] As mentioned above, Air Liquide has developed a technology thatis capable of altering the zeta potential of cellulose fibers using CO₂.M. Muguet and J. M. deRigaurd, “Improvements to Processes forManufacturing Paper Products by Improving the Physico-Chemical Behaviorof the Paper Stock”, International Publication No. WO 03/074788 A2. AirLiquide has also a pending patent application on such technology, Serie6052 which was filed as a U.S. provisional application on Sep. 30, 2002,bearing Ser. No. 60/414,876, and as a U.S. non-provisional on Sep. 6,2003, bearing U.S. Ser. No. 10/656,857. Applicant hereby expresslyincorporates by reference the entirety of these disclosures as if fullyset forth herein.

[0010] Generally in process control, a mathematical model is requiredcorrelating input parameters with output variations of the controlledsystem. To control wet-end parameters such as retention, drainage andformation by wet-end additives, a mathematical model correlating theadditive parameters with the zeta potential and cationic demand is firstrequired. Next, a mathematical model correlating the parametersaffecting flocculation such as zeta potential, cationic demand and thebridge forming capability of polymeric additives is needed. Sincenormally these input-output relationships are unknown, it is not easy toconstruct either a mathematical control model or a simulation model (F.Onabe). F. Onabe, MEASUREMENT AND CONTROL, Chapter 12. W. Scott explainsthat these are non-linear, interacting relationships. W. Scott,PRINCIPLES OF WET END CHEMISTRY, TAPPI Press, Atlanta, Ga., 1996. Wang,H. et al., describes a neural network that models the relationshipbetween the wet end chemicals and the properties of the resulting paper.H. Wang, B. Oyebande, “On the Application of Neural Networks Modeling toa Wet End Chemical Process in Paper Making,” IEEE Conference on ControlApplications—Proceedings 1995. IEEE, Piscataway, N.J., USA pp. 657-662,1995.

[0011] To implement a real-time control optimization scheme in the wetend, it is useful to have real-time measurements available. The commonlack of immediate feedback measurement about the effectiveness of theadsorption process is a serious shortcoming, and this leads to millpractices of minimizing input disturbances by controlling individualparameters. Most of these parameters are typically controlled, such aspH, ionic demand, consistency (Cy), flowrate, etc. However, thoseproperties that are not controlled due to the lack of on-lineinstruments present challenges. For example, ZP measurement is normallymeasured off-line. Most mills lack an on-line ZP analyzer, and so it isimpossible to attain an on-line ZP control or optimization.

[0012] Thus, a problem associated with paper processing methods thatprecede the present invention is that they do not provide a method ofmore closely controlling the performance of wet end chemistry in papermanufacture by controlled CO₂ addition to the wet end.

[0013] Still another problem associated with paper processing methodsthat precede the present invention is that they do not providecontrolled CO₂ addition into the wet end that permits the control ofunmeasured properties to improve the performance of wet end chemistry inpaper manufacture.

[0014] An even further problem associated with paper processing methodsthat precede the present invention is that they do not provide a controlmechanism for CO₂ addition into the wet end that permits the morereliable control of unmeasured properties, by providing a predictor ofdisturbances to the system that facilitates refinement of data.

[0015] The present invention seeks to overcome these problems while atthe same time providing a cost-effective, simply used mechanism forcontrolling CO₂ addition into the wet end of paper manufacture.

SUMMARY OF THE INVENTION

[0016] A method for controlling the CO₂ addition in a wet end processutilizing CO₂ addition is disclosed. A papermaking composition and CO₂are combined to create a CO₂ -enriched papermaking composition. At leastone electrical property of either the papermaking composition or of theCO₂ -enriched papermaking composition is either measured or estimated.The rate of addition of CO₂ to maintain the at least one electricalproperty within a pre-selected range of values is then controlled.

[0017] In one embodiment, the electrical property is selected from thegroup consisting of ZP, CD and ion concentration or any equivalentthereto, and is estimated by measuring at least one property of eitherthe papermaking composition or the CO₂-enriched papermaking compositionselected from the group consisting of flowrate, CD, ZP, ionconcentration, Cy, pH, conductivity and alkalinity and using a model.Preferably, the ZP is estimated. Thus, the measured property can bemeasured from either the papermaking composition or the CO₂-enrichedpapermaking composition, and is preferably measured from the papermakingcomposition. Likewise, the estimated electrical property can beestimated for either the papermaking composition or the CO₂-enrichedpapermaking composition, and is preferably estimated for theCO₂-enriched papermaking composition.

[0018] Various control schemes are employed to better control the CO₂addition by maintaining the at least one electrical property within apre-selected range of values.

[0019] Thus, it is an object of the present invention to provide amethod of more closely controlling the performance of wet end chemistryin paper manufacture by controlling the CO₂ addition to the wet end.

[0020] It is a further object of the present invention to provide acontrol mechanism for CO₂ addition into the wet end that permits thecontrol of unmeasured properties, thereby improving the performance ofwet end chemistry in paper manufacture.

[0021] It is still another object of the present invention to provide acontrol mechanism for CO₂ addition into the wet end that permits themore reliable control of unmeasured properties, by providing a predictorof disturbances to the system that facilitates refinement of data andhence better performance of wet end chemistry in paper manufacture.

[0022] These and other objects of the present invention will be apparentfrom the description of the invention that follows.

BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In the detailed description that follows, reference will be madeto the following figures:

[0024]FIG. 1 is a schematic diagram illustrating an embodiment of thecontrol method adapted to a specific papermaking process;

[0025]FIG. 2 is a schematic diagram illustrating another embodiment ofthe control method;

[0026]FIG. 3. is a schematic diagram illustrating the expectedperformance of a feed forward control responding to a normalized stepchange and a charge demand disturbance; and

[0027]FIG. 4 is a schematic diagram illustrating another embodiment ofthe control method adapted to a specific papermaking process.

DESCRIPTION OF PREFERRED EMBODIMENTS

[0028] A system and method for controlling the parameters in a wet endprocess by means of CO₂ injection in a real-time manner using anadvanced controller is presented. The design of the advanced controllermaintains the desired set point and rejects the influence of undesirablewet end disturbances. The effects of the disturbances on the wet end aremodeled, and their on-line measurements are used to compensate theaddition of CO₂. This disclosure provides an effective way ofcontrolling parameter in the wet end using multi-variable advancedcontrol and CO₂ gas.

[0029] As mentioned above, Air Liquide has developed a technology thatis capable of altering the zeta potential of cellulose fibers using CO₂.M. Muguet and J. M. deRigaurd, “Improvements to Processes forManufacturing Paper Products by Improving the Physico-Chemical Behaviorof the Paper Stock”, International Publication No. WO 03/074788 A2. AirLiquide has also a pending patent application on such technology, Serie6052 which was filed as a U.S. provisional application on Sep. 30, 2002,bearing Ser. No. 60/414,876, and as a U.S. non-provisional on Sep. 6,2003, bearing U.S. Ser. No. 10/656,857. Applicant hereby expresslyincorporates by reference the entirety of these disclosures as if fullyset forth herein.

[0030] The instant disclosure relates to a control method adaptabletherefor.

[0031] The alkalinity in water remains unaltered with the addition ofCO₂ due to the balance of carbonic species. However, when the CO₂ isadded in the presence of CaCO₃, the alkalinity is changed due to theextra production of bicarbonate.

[0032] The utilization of CO₂ has proven to improve the efficiency ofthe wet end process. The design of the application requires a goodknowledge of the interactions caused by the CO₂ and the extent of theseinteractions. This knowledge is covered theoretically by equilibriumanalysis of water chemistry. In order to maintain the efficiency of theprocess it is helpful to design control systems that keep the processrunning under the designed specifications and rejects majordisturbances. The most important disturbances can be attributed to thechange of concentration in the make up water, temperature, pressure,consistency, or other chemical addition variations. In order to designthe control system capable of rejecting these variations, it is helpfulto know the dynamic effect on the controlled variables and their dynamicrelationship with the CO₂ supply. These relationships are obtainedeither from available process knowledge, or dynamic tests in the mill,or theoretical models.

[0033] Dynamic modeling of the most important species in the aqueoussystem with gaseous CO₂ and CaCO₃ and its effect on Zeta Potential (ZP)and Charge Demand (CD) can be performed. The dynamic model assumed aconstant alkalinity.

[0034] The CO₂—CaCO₃ system is well studied in equilibrium conditions,but the studies are limited when it comes to dynamic (kinetic)conditions. When exploring the dynamic modeling of this system, oneneeds to consider a variety of parameters that play important roles,such as mass transfer and surface reactions. The operating conditionsunder which the CO₂—CaCO₃ are chosen to operate, define how fast theequilibrium conditions are met, and are worthwhile considering whendesigning a model-based control system. The most important effects ofvarious operating conditions such as partial pressure of CO₂,temperature, along with system-specific variables such as calciumcarbonate surface area and mass transfer coefficient, are also presentedhere.

[0035] The validation of the proposed models requires the off-linemeasurements of alkalinity and [Ca²+] which are tedious and timeconsuming. The potential for using conductivity measurements to predictthese off-line measurements is therefore considered.

[0036] MODEL DEVELOPMENT

[0037] Equilibrium

[0038] The dynamic behavior of the species in a CO₂—CaCO₃ system dependson several variables. The dynamic behavior will be represented in theform of ordinary differential equations (ODE), which require initialconditions in order to have their solution. Some of the initialconditions are known and measured in a typical (batch) experiment, suchas pH. However, other initial conditions are not known and rarelymeasured, such as [CO₃ ⁻²] concentration. Equilibrium studies canprovide the estimates of the values of any component for any givencondition assuming the conditions have not changed in order to reachequilibrium. Then, the equilibrium calculations can be used as initialconditions for ODE. Similarly, equilibrium studies can be used tocompare the final or steady state results of dynamic equations. Insteady state, the ODE results should be consistent with the equilibriumconditions at the new operating conditions.

[0039] The mass transfer coefficient, kx, has an impact on the timeresponse of the variables but does not affect the final steady state orequilibrium values. On the other hand, pCO₂ (partial pressure of CO₂)directly influences the equilibrium values. So, the value of the pCO₂that attains the experimental steady state parameters needs to be foundor closely monitored, if possible. In order to find the operating pCO₂that achieves the equilibrium conditions, an equilibrium problem is thensolved.

[0040] Following the example on p. 168 by Stumm & Morgan (Stumm, W. andMorgan, J. J. “Aquatic Chemistry: Chemical Equilibria and Rates inNatural Waters”, John Wiley & Sons, Third Edition, 1996), a Matlabprogram is utilized to solve the set of nonlinear algebraic equationsdefined by: $\begin{matrix}{\frac{\lbrack H^{+} \rbrack \lbrack {HCO}_{3}^{-} \rbrack}{\lbrack {H_{2}{CO}_{3}^{*}} \rbrack} = K_{1}} & (1) \\{\frac{\lbrack H^{+} \rbrack \lbrack {CO}_{3}^{2 -} \rbrack}{\lbrack {HCO}_{3}^{-} \rbrack} = K_{2}} & (2)\end{matrix}$

 [H₂CO₃*]=K_(H) pCO₂   (3)

[H⁺][OH⁻]=K_(W)   (4)

[Ca⁺²][HCO₃ ⁻]=K_(SO)   (5)

2[Ca]+[H³⁰ ]=[HCO₃ ⁻ ]+2[CO ₃ ²⁻]+[OH⁻]  (6)

[0041] The equilibrium constants are reported in the literature.Correlations for temperature dependent equilibrium constants (Stumm &Morgan) Temp 294.45 21.3 A1 A2 A3 A4 A5 LogK1 −6.374687 −356.3094−0.06092 21834 126.8339 −1684915 LogK2 −10.36285 −107.8871 −0.0325285151.79 38.92561 −563713.9 LogKH −1.423209 108.3865 0.019851 −6919.53−40.45154 669365 LogKw −14.12347 −283.971 13323 −0.050698 102.2445−1119669 LogKso −8.459868 −171.9065 −0.077993 2839.319 71.595 0

[0042] T (deg C.) LogK1 LogK2 LogKH LogKw LogKso 20 −6.383133 −10.37557−1.406868 −14.16818 −8.453297 25 −6.353105 −10.32885 −1.46794 −13.99953−8.47983 30 −6.329367 −10.28788 −1.524416 −13.83949 −8.509751 35−6.311358 −10.25227 −1.576641 −13.68751 −8.543034 40 −6.298577 −10.22169−1.624926 −13.54308 −8.579652 45 −6.290573 −10.19583 −1.669556 −13.40575−8.619574 50 −6.286946 −10.1744 −1.710789 −13.2751 −8.662766 55−6.287334 −10.15714 −1.748859 −13.15074 −8.709195 60 −6.291415 −10.14381−1.783981 −13.03233 −8.758826 65 −6.298898 −10.13418 −1.816351 −12.91953−8.81162 70 −6.309522 −10.12806 −1.846147 −12.81207 −8.867541

[0043] Equations (1)-(6) describe the equilibrium equations of theCO₂—CaCO₃ in water at a given CO₂ pressure, pCO₂. These equations can bemanipulated in different forms to fit different conditions. Forinstance, if the calcium is not in equilibrium, then equation (5) is notapplicable, and the [Ca⁺²] is estimated from a rate equation.

[0044] Kinetics (Rate)

[0045] The equilibrium studies determine the steady state conditions orthe total changes based on operating conditions. On the other hand,kinetic studies determine also the rate at which changes occur. Processcontrol design depends on both results, the extent of the change and therate of change. The exchange of CO₂ from the gas phase to the bulkliquid for constant alkalinity is presented as the diffusion equation:$\begin{matrix}{\frac{C_{T}}{t} = {{{klx}( {{p_{Co2}H} + {Alk} - C_{T}} )} = R_{CO2}}} & (7)\end{matrix}$

[0046] where,

[0047] C_(T)=Total carbonic species, M=[H₂CO₃*]+[HCO₃ ⁻]+[CO₃ ⁻²]

[0048] klx=Mass transfer coefficient, min⁻¹

[0049] pCO2=CO₂ partial pressure in the gas, atm

[0050] H=Henry's equilibrium constant

[0051] Alk=Alkalinity, M (mol HCO_(3/L))

[0052] Equation (7) is valid when the concentration of [CO³⁻⁻] isnegligible and C_(T)>>Alk. This occurs when the pressure issignificantly higher than the partial pressure of CO₂ in the atmosphere.For pressures close to atmospheric, Equation (7) is not valid, but it isassumed that the operating conditions where it will be used are in CO₂rich conditions.

[0053] If the alkalinity is not constant, then the rate of transfer ofCO₂ moles converted to [H2CO₃*] is $\begin{matrix}{\frac{\lbrack {H_{2}{CO}_{3}^{*}} \rbrack}{t} = {{\frac{\quad}{t}\lbrack {C_{T} - \lbrack {HCO}_{3}^{-} \rbrack} \rbrack} = {\frac{C_{T}}{t} - \frac{\lbrack {HCO}_{3}^{-} \rbrack}{t}}}} & (8)\end{matrix}$

[0054] then, the rate of total carbonic species becomes $\begin{matrix}{\frac{C_{T}}{t} = {{R_{{CO}_{2}} - \frac{\lbrack {HCO}_{3}^{-} \rbrack}{t}} = {R_{{CO}_{2}} - \frac{{Alk}}{t}}}} & (9)\end{matrix}$

[0055] In order to estimate the time dependant variation of pH, onestarts from the relationship: $\begin{matrix}{\lbrack H^{+} \rbrack = {( \frac{{pK}_{1}}{Alk} )( {C_{T} - {Alk}} )}} & (10)\end{matrix}$

[0056] which can be rewritten as: $\begin{matrix}{\lbrack H^{+} \rbrack = {{{pK}_{1}\frac{C_{T}}{Alk}} - {pK}_{1}}} & (11)\end{matrix}$

[0057] Taking the derivative with respect to time on Equation (11)reveals that the equation is more complex when considering a timedependent alkalinity: $\begin{matrix}{\frac{\lbrack H^{+} \rbrack}{t} = {{pK}_{1}\frac{}{t}( \frac{C_{T}}{Alk} )}} & (12)\end{matrix}$

[0058] This becomes, $\begin{matrix}{\frac{\lbrack H^{+} \rbrack}{t} = {{pK}_{1}\{ \frac{{{Alk}*R_{CO2}} - {C_{T}d\quad {Alk}}}{{Alk}^{2}} \}}} & (13)\end{matrix}$

[0059] The evaluation of Equation (13) depends on Equation (9) orR_(CO2), but also depends on dAlk/dt. To the present time, an analyticalexpression for dAlk/dt has not been found.

[0060] One tentative expression can be derived from the simplifiedproton balance expression when CO₂is added in a system in the presenceof CaCO₃:

2[Ca⁺⁺]˜=Alk   (14)

[0061] Even though Equation (14) is an equilibrium equation for protonbalance, it can be used as an approximate relationship between calciumions and alkalinity at all times. Hence, taking the time derivative inboth sides, $\begin{matrix}{\frac{{Alk}}{t} = {2\frac{\lbrack {Ca}^{++} \rbrack}{t}}} & (15)\end{matrix}$

[0062] The implementation of Equations (13) and (15) has posedimplementation problems and the results have not been successful to thispoint due to numerical reasons. When solving Equations (13) and (15)simultaneously, the hydrogen proton concentration becomes non-real. So,a simplification is presented.

[0063] It is known that the proton-transfer reactions such as thecarbonic reactions are usually very fast with half-lives less thanmilliseconds. This suggests that it may not be necessary to express inODEs the equations to estimate the hydrogen proton or the alkalinity.Instead, as the rate limiting equations are solved in ODEs, the rest ofthe chemical species can be determined solving the appropriateequilibrium equations.

[0064] Equations (9), (13) and (15) describe the kinetic equations ofC_(T), pH and Alk, correspondingly. The calcium dissolution kineticsobtained by Plummer et. al. has the form:

R _(Ca) =k _(Ca,1) a _(H) +k _(Ca,2) a _(H2CO3) +k _(Ca,3) a _(H2O) −k_(Ca,4) a _(Cu) a _(HCO3)   (16)

[0065] Plummer, L. N., Wigley, T. M., and Parhurst, D. L. “The kineticsof calcite dissolution in CO₂— water systems at 5° to 60° C. and 0.0 to1.0 ATM CO₂”, American Journal of Science, Vol. 278, p. 179-216,February, 1978. The activity coefficients, a_(i), are equal toconcentrations. At 25° C., the parameters are:

[0066] k_(Ca,1)=5.115e−02;

[0067] k_(Ca,2)=3.4247e−05;

[0068] k_(Ca,3)=1.1919e−07;

[0069] k_(Ca,4)=4.55e−02;

[0070] The units of R_(Ca) are in mmol/(sec⁻¹cm²). The constantsk_(Ca,i) are temperature dependent and k_(Ca,4) is the backwardreaction. Besides converting R_(Ca) to mol and min⁻¹, the kineticexpression depends on the total surface area of the calcite particles.Denoting the particle area as a_(c), defined as the surface area perunit of mass, provides the calcium dissolution in mol/min as:$\begin{matrix}{\frac{\lbrack {Ca}^{+ 2} \rbrack}{t} = {{a_{C}\lbrack {CaCO}_{3} \rbrack}V\quad R_{Ca}\quad ( {60/1000} )}} & (17)\end{matrix}$

[0071] The product [CaCO3]V corresponds to the total grams of CaCO3 inthe reactor. Plummer reports a range of polished calcite particles up to90 cm²/gr.

[0072] The rate expressions of CO₂ transfer and calcium dissolutions arethe phenomena that dictate the global rates. Hence, it is suggested thatin order to identify the time dependant values of all the species in aCO₂—CaCO₃ system, small increments solving the ODEs of CO₂transfer andcalcium dissolution (Equations (9) and (17)) will return the [Ca⁺²] andtotal carbon species, C_(T). Then, the following algebraic equations aresolved to find alkalinity, [HCO₃], and hydrogen proton, [H⁺]:$\begin{matrix}{\frac{\lbrack H^{+} \rbrack \lbrack {HCO}_{3}^{-} \rbrack}{\lbrack {H_{2}{CO}_{3}^{*}} \rbrack} = K_{1}} & (18) \\{\frac{\lbrack H^{+} \rbrack \lbrack {CO}_{3}^{2 -} \rbrack}{\lbrack {HCO}_{3}^{-} \rbrack} = K_{2}} & (19)\end{matrix}$

 [H⁺][OH³¹ ]=K_(W)   (20)

C_(T)=[H₂CO₃*]+[HCO₃ ⁻]+[CO₃ ²⁻]  (21)

2[Ca]+[H⁺]=[HCO₃ ⁻]+2[CO₃ ²⁻]+[OH⁻]  (22)

[0073] Once these equations are solved, the new values are used to solvethe next increment of the ODEs.

[0074] The dynamic modeling of the CO₂—CaCO₃ is then defined by 2 ODEs(Equations (9) and (17)), and the simultaneous solution of algebraicequations (Equations (18) through (22)). All these equations have avariety of parameters that have to be specified prior to the numericalsimulations. These parameters are the temperature, mass transfercoefficient, the Co₂partial pressure, and calcium carbonate surfacearea.

[0075] All the kinetic and equilibrium constants are temperaturedependent. The temperature dependence of the kinetic parameters havebeen presented in a previous report (CRC200343) and have shown above forT=25° C. The temperature dependence of the equilibrium parameters isshown in Appendix A.

[0076] Experiments

[0077] A series of experiments was performed. The experiments utilized8.125 gr of CaCO₃ (equivalent to 20% PCC in pulp) in a 1.3 L of DIwater. Two types of CaCO₃ were used: ALBACAR HO PCC (Specialty Minerals,Inc) and reagent grade CaCO₃ (Fisher Scientific). The CaCO₃ stocksolution was agitated for 24 hours to reach equilibrium with the CO₂inthe atmosphere. The initial sample (time zero) was taken from the stock.1.3 L of the stock was placed in the reactor and agitation was set at1500 rpm. Timing started when the dosing of CO₂ started. The totalamount of CO₂ was 10.256 Kg/ton assuming a 2.5% Cy slurry, or 2.6e⁻⁰⁴ KgCO₂/L. Dosing of CO₂ was completed in approximately 40 seconds. Thedosage was performed in order to obtain a constant pCO₂ pressure in thereactor head. Close to 10-milliliter samples were withdrawn andimmediately filtered with 0.02-micrometer filters. Several experimentswith the same conditions were run in order to take more samples.Conductivity, pH, alkalinity and calcium concentration, were measuredfrom each sample.

[0078] Experimental Results

[0079] Table 1 shows the experimental results obtained at ˜24° C. usingALBACAR PCC. Notably, the concentrations of calcium and alkalinityincrease rapidly to reach equilibrium values in a few minutes.

[0080] From the proton balance indicated in Equation (6), and since theconcentration of carbonate, [CO³⁻⁻], is negligible at this pH, therelation 2*[Ca⁺²]˜=Alk must be satisfied (Stumm & Morgan). From theexperimental results shown in Table 1 it can be seen that thisrelationship is not satisfied. These results represent much highervalues of alkalinities compared to the calcium dissolved equilibrium.These results gave the indication that the ALBACAR PCC might have somechemicals that affect the CO₂—CaCO₃ equilibrium

[0081] Table 2 shows the experimental results using reagent grade CaCO₃.As with ALBACAR, the concentrations of calcium and alkalinity increasevery rapidly towards equilibrium. More in depth explanations on thisbehavior will be presented later. What is interesting regardingequilibrium is the fact that the relationship between the equilibriumcalcium and alkalinity is much closer to meeting the relationship2*[Ca⁺²]˜=Alk. Excluding the 1-minute sample, the experimental valueshave an average error of 5% from the analytical expression. The highererror at 1 minute is attributed to the difficulty to take arepresentative sample at such an early stage in the experiment.

[0082] It was noticed that the pH variation of the filtered samplesduring the experiment was too small between time zero and the lastsample. The pH measurements of the samples before filtering were closerto the expected according to equilibrium analysis.

[0083] The results shown in Table 2 are utilized in the remaining ofthis study to compare with the equilibrium and dynamic models.

[0084] Equilibrium Analysis of Results

[0085] The equilibrium equations allow determining the target steadystate conditions of CO₂—CaCO₃ systems. With this information, one canfind in advance what steady state values are expected in experiments andin dynamic models simulations.

[0086] The first step to confirm the validity of the problem set up andits results, consisted in duplicating the problem on p. 186 by Stumm &Morgan. The problem determines the equilibrium concentrations in theCO₂—CaCO₃ system in the presence of atmospheric pressure (10^(−3.5)atm=3.16e−04 atm). The solution of this problem was implemented inMatlab (Mathworks, Inc) using a nonlinear algebraic equation solvercommand. The results obtained in Matlab solving the set of equations (I)through (6) are [Ca]=4.636e−04 M; Alk=9.2721 e−04 M and pH=8.3048. Notealso that 2[Ca²⁺]˜=Alk.

[0087] In order to compare the experimental results obtained with CaCO₃with the equilibrium equations, the partial pressure of CO₂ is needed.This pressure has not been reliable or available experimentally. Someearly measurements indicated that the partial pressure of CO₂ at thebeginning of the experiment was around 0.43 psig, equivalent to 0.02atm, but it declined continuously and its recording was unreliable.Furthermore, the partial pressure characteristic to the system inequilibrium, as represented in Equation (3), assumes to be constant.This is not the case in the experimental apparatus as the system is abatch reactor and variables change with time. However, in order to makethe equilibrium equations, one has to find the characteristic CO2partial pressure that attains the same experimental equilibriumconditions. Table 3 shows a set of results obtained when solvingEquations (1) through (6) for a range of CO₂ partial pressures.

[0088] Comparing the equilibrium results obtained from equilibriumequations as shown in Table 3 (with extrapolation), and the experimentalresults from Table 2, it is obtained that the equilibrium conditionsthat match the experimental results are:

[0089] CASE A: Theoretical Equilibrium at 25° C.

[0090] i. Alk=5e−03 mol HCO₃/L=250 mg CaCO₃/L=250 ppm CaCO₃

[0091] ii. [Ca]=2.5e−03 mol Ca/L=100 mg Ca/L

[0092] iii. pCO2=10^(−1.049) atm=˜0.09 atm

[0093] iv. pH=6.5 (Matlab), 6.9-7.0 PHREEQ

[0094] The experimental results using ALBACAR HO (Specialty Minerals,Inc.) suggested that the equilibrium indicator to match was the pH. Butthe partial pressure of CO₂ that achieves a 7.3 equilibrium pH achievesa lower theoretical alkalinity than the experimental values. Thetheoretical equilibrium conditions for this case are labeled as CASE Band are shown below. At this point, it was suspected that the differencein results could be due to the unknown components in the PCC used(ALBACAR HO, Specialty Minerals, Inc).

[0095] CASE B: Final Equilibrium Experimental Results (Dec. 12, 2003)

[0096] i. pH=7.3

[0097] ii. [Ca]=106 ppm=2.7e−03 M

[0098] iii. Alk˜=300 ppm as CaCO3=6e−03 mol [HCO3]/L

[0099] iv. Initial pCO₂˜0.4 psig (±0.2 psig)=2.72e−02 atm

[0100] Even though the equilibrium pH values in the theoretical andexperimental cases are the same, the calcium and alkalinityconcentrations deviate significantly. The experimental calciumconcentration almost doubles the theoretical. The theoreticalequilibrium calcium concentration depends on the constant K_(SO). Asidefrom experimental errors, one possibility for the discrepancy is thatthe CaCO₃ utilized is either not pure or different. Based on theexperimental results, and combining some of the previous equations, onecan obtain: $\begin{matrix}{\lbrack {CO}_{3}^{- 2} \rbrack = {\frac{K_{1}K_{2}K_{H}p\quad {CO}_{2}}{\lbrack H^{+} \rbrack^{2}} = {{2.8637e} - {06M}}}} & (23)\end{matrix}$

[0101] Substituting in Equation (5) one gets the equilibrium constantK_(SO), using the experimental calcium concentration (2.65e−03 M):

K_(SO)=[Ca⁺²][HCO₃ ⁻]=7.588e−09=10^(−8.1198)   (24)

[0102] This results in a K_(SO), almost twice the reported in theliterature. Running the equilibrium software for the new K_(SO) and theother constants at 21° C., the following results are obtained:

[0103] CASE C: Theoretical with new K_(SO)

[0104] i. pH=7.3061

[0105] ii. pCO₂₌₁₀ ^(−1.985) atm=1.0351e−02 atm

[0106] iii. [Ca]=2.2e−03 M=89.75 ppm

[0107] iv. Alk=4.5e−03 M=274.5 ppm

[0108] Although the predicted equilibrium calcium concentration is nowcloser to the experimental, the alkalinity estimation is negativelyinfluenced. The summaries of the results are shown in the followingtable. T pCO₂ Case (° C.) (atm) pH [Ca] (M) Alk (M) Comments Text 2510^(−3.5) 8.304 4.636e-04 9.2721e-04 As shown in Morgan Text 2510^(−3.5) 8.304 4.636e-04 9.2721e-04 Duplicated in Matlab A 2510^(−1.04) 6.8 2.5e-03 5e-03 Theoretical B 21.3 0- 7.3 2.7e-03 6e-03ALBACAR 10^(−1.45) PCC Experi- ment C 21.3 10^(−1.985) 7.306 2.2e-034.5e-03 New Kso D 21.3 10^(−2.05) 7.3 1.4e-03 2.8e-03 Theoretical E 25N/A 7.1 (?) 2.46e-03 5.08e-03 Grade CaCO3 ex- periment

[0109] The table shows that the experimental results with chemical gradeCaCO3 meet the calcium and alkalinity relationship consistently (CASEE). Hence, the dynamic experimental data from this experiment will beused to compare them with the dynamic models. The complete set ofoperating conditions, such as the pCO₂, will be used from theequilibrium calculations (CASE A).

[0110] Kinetic (Rate) Analysis of Results

[0111] The mass transfer coefficient, kx, in Equation (9) defines thespeed at which gaseous CO₂ is transferred to the liquid. It depends onphysical properties and equipment design. Several correlations can befound in the literature for specific designs and operating conditions.Based on published literature, a typical mass transfer coefficient in anagitated tank where the gas is bubbled near the stirrer is in the orderof 0.2 min⁻¹. This number was used as a reference for the nextsimulation.

[0112] It was found that the experimental results shown in Table 2 arethe equilibrium conditions when the partial pressure is 0.09 atm. Thispressure will be utilized as the nominal operating pressure.

[0113] Finally, the surface area is needed to determine the dissolutionrate according to Equation (16). The surface area of the ALBACAR OH(Specialty Minerals, Inc) was found to be equal to 11.5 m²/gr (11.5e+04cm²/gr) with mean diameter sizes of ˜1.6 micrometers. On the other hand,the CaCO3 from Fisher has a mean diameter of 30 to 50 micrometers. Thismay represent a surface area in the range of 10⁴ cm²/gr. Note that themaximum surface area of the calcium carbonate reported on the calciumdissolution paper by Plummer et. al. is 90 cm²/gr, which is severalorders of magnitude smaller compared to the calcium carbonate tested atCRC. The consequence of the surface area in calcium dissolution andoverall kinetics is presented later on.

[0114] Dynamic Model Test

[0115] Using the nominal operating conditions:

[0116] i. pCO₂=0.09 atm

[0117] ii. kx=0.2 min⁻¹

[0118] iii. T=25° C.

[0119] iv. a_(c)=calcium carbonate surface area=10³ cm²/gr

[0120] This set of conditions will be labeled as Conditions Set A

[0121] The initial conditions correspond to the equilibrium with theatmospheric CO₂ partial pressure (10^(−3.5) atm): pH=8.96;Alk=3.3e−04molHCO₃/L; [Ca⁺²]=1.65e−04 mol Ca/L; C_(T)=3.45e−04 mol/L. Inthis report, all the alkalinities are expressed on mol/L, meaning mol[HCO³⁻]/L, and the calcium will be expressed in mol/L, meaning mol Ca/L.

[0122] Table 4 shows the simulation model using the condition Set Acompared to the experimental values. The steady state predictions of themodel match the experimental values when the nominal partial pressure ofCO₂ was lowered from 0.09 atm to 0.07 atm. This difference can beattributed to loss of accuracy when discretizing the dynamic models inorder to solve it with equilibrium equations. The solution shown inTable 4, furthermore, was difficult to achieve, as it required some“troubleshooting”. When solving the ODE's (Equations (9) and (17)), itwas noticed that the solution of dCa/dt was resulting in [Ca²⁺] valueshigher than the values that could be obtained in equilibrium. Thedynamic solution of dCa/dt in this system cannot resolve in higherconcentrations than equilibrium. Under steady state conditions, dCa/dtshould only equalize the equilibrium predictions. This problem led toconclude that kinetic expression in Equation (16) over predicts thecalcium dissolution when the calcium carbonate surface area issignificantly higher than the one used by Plummer et. al. (90 cm²/gr).

[0123] When the calcium carbonate surface area is high (˜10⁴ cm²/gr andhigher), the calcium dissolution is so fast that it approachespractically instantaneously to equilibrium, which makes this reaction asfast as the proton-transfer reactions. The fast calcium dissolution thensuggests to calculate the calcium at any specific time using theequilibrium equation as given by Equation (5), simultaneously with theother proton-transfer reactions. So, for high surface areas, only onedifferential equation is solved in each time interval (dC_(T)/dt). OnceC_(T) is known from Equation (9) at one sample interval, the followingequations are solved to find the equilibrium calcium concentration:$\begin{matrix}{K_{1} = \frac{\lbrack H^{+} \rbrack \lbrack {HCO}_{3}^{-} \rbrack}{\lbrack {H_{2}{CO}_{3}^{*}} \rbrack}} & (25) \\{K_{1} = \frac{\lbrack H^{+} \rbrack \lbrack {HCO}_{3}^{-} \rbrack}{\lbrack {H_{2}{CO}_{3}^{*}} \rbrack}} & (26)\end{matrix}$

 K_(s)=[Ca²⁺][CO₃ ²⁻]  (27)

C_(T)=[H₂CO₃*]+[HCO₃ ⁻]+[CO₃ ²⁻]  (28)

[0124] These equations can be combined to find [Ca²⁺] as a function ofC_(T) only: $\begin{matrix}{C_{T} = {{\frac{4K_{2}}{K_{1}K_{s}}\lbrack {Ca}^{2 +} \rbrack}^{3} + {2\lbrack {Ca}^{2 +} \rbrack} + \frac{K_{s}}{\lbrack {Ca}^{2 +} \rbrack}}} & (29)\end{matrix}$

[0125] Equation (29) is faster to solve since does not require initialvalues to iterate, as is the case of solving simultaneous nonlinearalgebraic equations. The simulation results in Table 4 show the calciumcalculations from equilibrium, as the kinetics predictions were higherthan equilibrium, which is not believed to be possible.

[0126] The temperature and partial pressures of CO₂ affect the rate ofdissolution, but also the equilibrium conditions. At this point, one isonly interested in changing the rate, while keeping the equilibrium(steady state) results according to experimental results. The onlyavailable parameter than can achieve this goal is the mass transfercoefficient. The experiments were carried out at very high speeds (1500rpm), but the mass transfer coefficient is not known. If the masstransfer coefficient is increased from 0.2 min⁻¹ to 2.0min⁻¹, the CO₂ istransferred faster to the bulk and the proton-transfer reactions occurearlier.

[0127] Table 5 shows the simulation results with the higher masstransfer coefficient. It can be seen now that the experimental resultshave much better agreement with the simulations.

[0128] In conclusion, the dynamic modeling of the CO₂—CaCO₃ system hasbeen developed to represent the experimental results obtained at CRC.However, it must be emphasized that in order to have good modelingresults, knowledge of the right operating conditions, such as partialpressure, and mass transfer coefficient, along with the nature of thecalcium carbonate, have to be considered in order to have the best modelrepresentation. The experimental example has allowed illustrating someof the important features of the modeling. Next, a more detailedexplanation of the modeling issues will be shown.

[0129] Surface Area

[0130] The calcium dissolution kinetics is controlled by surfacereaction, which leads to the importance of the surface area. It wasalready shown that for high surface calcium carbonate, a goodapproximation is to disregard the calcium rate predictions and use theequilibrium equations instead. Nevertheless, a deeper insight on thecalcium dissolution in case the surface area is small is presented. Fromnow on, several simulations will be shown using the conditions definedin the following condition Set B:

[0131] Condition Set B:

[0132] i. pCO₂=0.025 atm

[0133] ii. kx=0.2 min⁻¹

[0134] iii. T=25° C.

[0135] iv. a_(c)=1e+0.5 cm ²/gr

[0136] Table 4 and Table 5 show simulations that assume that the calciumsurface is significantly high (10⁴ cm²/gr+), which makes the dissolutionevolve so fast that reaches equilibrium almost instantly and the calciumis calculated from equilibrium equations. Table 6 shows simulations whenthe surface area is smaller and then the calcium dissolution isdescribed by the kinetic equation reported by Plummer et al.

[0137] In general, it can be seen that the lowest surface area (90cm²/gr) takes several orders of magnitude longer to reach equilibrium.The highest surface area simulated of 9e+04 cm²/gr was implementedcombining the equilibrium equations and the kinetic equations. At thebeginning of the simulation and until approximately 5 minutes, the ratepredictions were higher than the equilibrium, which is not possible, sothe equilibrium predictions are reported. After 5 minutes, the ratepredictions were lower than the equilibrium, and hence the ratepredictions by Plummer et. al. are plotted. The switching between onemodel and another causes some numerical discrepancies shown as spikes inthe simulations.

[0138] Note the effect that the surface area has on pH. A high surfacearea enhances the calcium dissolution and the proton transfer equationsequilibrate to lower [H+] concentration (high pH). On the other hand,when the surface area is small, the calcium dissolution is very slow andthe equilibrium concentration for the proton-transfer species, such as[H+], is similar to when barely there is calcium. For this reason, Table6 shows the simulation when there is practically no calcium and there isno CaCO₃ to dissolve. When CaCO₃ is absent, the alkalinity and calciumremain constant, and the pH drops rapidly to lower steady state values.

[0139] Table 7 shows a closer view of the pH of Table 6. It is moreclearly seen that when the surface area is small at initial times, thesystem behaves as if there was no calcium dissolution and the pHdecreases rapidly. When the calcium concentration starts building up,then the pH starts increasing towards the corresponding equilibrium withCaCO₃.

[0140] Mass Transfer Coefficient

[0141] The mass transfer coefficient does not affect the steady state orequilibrium conditions. It only affects how fast the equilibrium isreached, just as the calcium carbonate surface area. From the processcontrol point of view, these variables have an effect on the timeconstant of the process and not the gain. Table 8 shows the effect ofdifferent mass transfer coefficients in all the variables.

[0142] Temperature

[0143] One factor that affects the equilibrium conditions is thetemperature of the system. All the equilibrium and kinetic constants aretemperature dependent, and any variation will have an impact on all theconcentrations. Table 9 shows a couple of simulations at differenttemperatures. The highest temperature shown (50° C.) drives thereactions towards lower calcium dissolution. The values of theequilibrium constants in Appendix show that the temperature affects theconstants K₁, K₂ and K_(s) in different directions.

[0144] Regarding the sensitivity of the variables with respect totemperature, Table 9 shows that the temperature has a bigger effect onthe concentrations than on pH. The small change in pH, however,represents a big change in the [H+] concentration change (because of thelogarithmic relationship). If small temperature changes occur in themill, big performance changes are expected when using CO₂

[0145] CO₂ Partial Pressure

[0146] Table 10 shows the effect of the CO₂ partial pressure on theCO₂—CaCO₃ system. The increase in the partial pressure promotes thetransfer of CO₂, the pH reduction and the calcium dissolution. Thepartial pressure also has a direct impact on the steady state conditions(equilibrium). Unlike temperature, the relatively smaller changes in theCO₂ partial pressure, the effect on all variables, including the pH, isgreater. This remains as the most important manipulating variable thatspecifies the final operating conditions.

[0147] Conductivity

[0148] During the experiments using ALBACAR OH (Specialty Minerals,Inc), the on-line conductivity measurements were recorded. Table 11shows the on-line conductivity measurements of one of the CO₂—CaCO₃experiments using ALBACAR PCC (Specialty Minerals, Inc). Conductivity isa measure of the ability of an aqueous solution to carry an electriccurrent. The ability depends on the presence of ions; on their totalconcentration, mobility, and balance; and on the temperature ofmeasurement. A general theoretical method to calculate the conductivityis presented by Clesceri et al. Clesceri, L. S., Greenberg, A. E., andEaton, A. D. “Standard Methods for the Examination of Water andWastewater”, 20^(th) Edition, APHA, AWWA, WEF. First, the infinitedilution conductivity is calculated:

k ⁰ =Σ|z _(i)|(λ_(−i) ⁰)(mM _(i))+Σ|z _(i)|(λ_(−i) ⁰⁾⁽ mM _(i))   (30)

[0149] where:

[0150] |zi|=absolute value of the charge of the i-th ion

[0151] mMi=millimolar concentration of the i-th ion

[0152] □⁰ _(+i), □⁰ _(−i)=equivalent conductance of the i-th ion

[0153] Then, calculate the ionic strength, IS in molar units:

IS=Σz _(i) ²(mM _(i))/2000   (31)

[0154] The monovalent ion activity coefficient, y, is calculated usingthe Davies equation for IS<=0.5M and for temperatures from 20 to 30° C.$\begin{matrix}{{y = 10^{{- 0.5}{({a - {0.3/S}})}}};{a = \frac{{IS}^{0.5}}{1 + {IS}^{0.5}}}} & (32)\end{matrix}$

[0155] Finally, the conductivity is calculated as:

k _(calc) =k ⁰y²   (33)

[0156] Equivalent ionic conductivities in aqueous solutions can be foundin different sources, including Lange's Handbook of Chemistry. Dean, J.A. “Lange's Handbook of Chemistry”, McGraw-Hill, Thirteen Edition. Theequations to calculate the conductivity as a function of the molarconcentration of the ions in solution are then used to “back-calculate”the ion concentrations based on the conductivity measurements. Since DIwater was used in the experiments, it is known that only two maincomponents can be found in the solution: [Ca²⁺] and [HCO3⁻]. However,there are an infinite number of ion concentration combinations that canproduce the same conductivity. For this, an additional relationship isneeded. The proton balance equation in a CO2—CaCO3 for the range of pHof interest, is simplified as

2[Ca²⁺]˜=[HCO3⁻]=Alk   (34)

[0157] Then, an optimization problem to calculate the concentration ofthe [Ca⁺²] and [HCO3⁻] ions is used and defined as: $\begin{matrix}{{\min\limits_{{\lbrack{Ca}^{2 +}\rbrack},{\lbrack{HCO}_{3}^{-}\rbrack}}\quad J} = {\min ( {k_{\exp} - {\hat{k}}_{calc}} )}^{2}} & (35)\end{matrix}$

[0158] such that Equation (32) is true. The back calculation is solvedby minimizing the objective factor, J. This factor consists of thesquared error of the measured or experimental conductivities, k_(exp),and the estimation of the calculated conductivities from Equation(k_(calc)). The solution will be the minimization of the problem thatmeets the proton balance equation. This problem is solved numerically inMatlab with the minimization of a constrained multivariable function.

[0159] Table 12 shows the experimental on-line conductivity measurementsand off-line [Ca²⁺] and alkalinity measurements of an experiment usingALBACAR PCC (Specialty Minerals, Inc). Aside from the first off-linesample, which may be considered inaccurate due to sampling difficulties,the calcium predictions from the conductivity measurements match veryclose the off-line experimental measurements. The alkalinities, on theother hand, have larger estimation errors. The maximum error is up to 40units.

[0160] Table 13 shows the estimations of [Ca ²⁺] and alkalinity of theexperiment using chemical grade CaCO3. The calcium estimates are almostas good as in the previous case. The alkalinities, on the other hand,have smaller prediction errors. This suggests that this experimentconsists of ions closer to the expected. The experiment with ALBACARcould have some components or ions that affect the conductivity, and maydrive Equation (32) off. In summary, it can be said that theconductivity measurement has the potential to predict the evolution ofthe most important ions in the CO₂—CaCO₃ system.

[0161] In the preferred embodiments thus described, phenomena that helpdetermine the rate of species in a CO₂—CaCO₃ system are the CO₂ transferand calcium dissolution. The other reactions are proton-transferreactions that occur quickly and can be considered in equilibrium,including the alkalinity. This disclosure presents the calculation ofthe proton-transfer reactions calculated and updated at everyintegration step of the rate equations.

[0162] The calcium dissolution can be calculated with equilibriumequations if the calcium carbonate surface area is significantly large(over 10⁴ cm²/gr). The CaCO₃ used in the experiments of this report havehigh surface areas and the best predictions results consideredequilibrium calculations of calcium. The increase of alkalinity with thesupply of CO₂ has a big impact on the pH, and hence on the calciumdissolution.

[0163] Once the alkalinity was calculated in a time dependent manner,the CO₂—CaCO₃ system was simulated for a variety of conditions in CO₂partial pressure, temperature, mass transfer coefficient and calciumcarbonate surface area. If the calcium carbonate surface area is large,the most important factor that controls the rate of the system is themass transfer coefficient. If the surface area is small (large particlediameters), the time constant of the system can be increaseddramatically due to slower calcium dissolution rate.

[0164] Unlike the mass transfer coefficient and the particle surfacearea, the temperature of the system and the CO2 partial pressure have aneffect on the equilibrium (steady state) conditions. The partialpressure has a bigger impact on the equilibrium conditions thantemperature, so it is important to have a well-controlled operation ofCO₂.

[0165] Finally, it is shown that the conductivity measurements can beused to predict the calcium and alkalinity of CO₂—CaCO₃ systems. A moredetailed development would be needed if other ionic species werepresent.

[0166] Referring now to FIG. 1, a schematic diagram illustrating anembodiment of the control method adapted to a specific papermakingprocess is shown. A mixing chest 1 receives a regulated inlet flow ofCO₂ and a papermaking composition such as a fiber flow, 7, and providesa CO₂—enriched papermaking composition, such as an outlet fiber flow.Properties of the fiber flow such as, for example, flowrate, CD (chargedemand), ZP (Zeta Potential), ion concentration, Cy (consistency), pH,conductivity and alkalinity are measured on-line before the fiber flowreaches the mixing chest, and measurements 2 are generated. At the sametime, on-line properties of the outlet fiber flow are measured byinstrument 3, and can be chosen from the same set of properties asdescribed above. An advanced controller, in this case a feed forwardcontroller, uses the measurements of the inlet flow and compensates thefeedback controller, 5, by adding the controller outputs, 6. Theresulting controller output is used to manipulate the inlet CO₂ thatwill maintain the desired wet end properties while minimizing variationsin the inlet fiber flow.

[0167] Note that certain properties can be described as electricalproperties, such as ZP, CD and ion concentration. Since an ion is anatom or molecule which has gained or lost one or more electrons, itthereby has a net negative or positive electrical charge. For example, afusion plasma is so hot that virtually all the electrons are strippedfrom the atoms creating ions that have a net positive charge equal tothe number of protons in their nucleus. Ion concentration is related tothe amount of such ions in per unit volume. Thus, there is a direct linkof a concentration of ions having an electrical charge.

[0168] However, if there are two different ions A and B withconcentration [A] and [B] mixed in a solution, there is still a totalelectrical charge, but measuring this electrical charge, for examplewith a conductivity meter in the solution, will not enable distinctionand measurement of [A] and [B]. The present disclosure anticipatesseparately distinguishing and measuring [A] and [B] individually. It isto be generally noted that ion concentration, as used herein,anticipates performing this operation where desired.

[0169]FIG. 2 shows the block diagram for the feed forward controller. Itrequires the mathematical relationship between the disturbance and thewet end measure, in this case the Zeta Potential (ZP), GL, and therelationship between the input CO₂ and the same wet end measure, Gp. Theadvanced controller design consists on finding the mathematicalrelationship of the feed forward controller F, and the feedbackcontroller Gc.

[0170] This embodiment is applicable in the wet end of pulp mills tocontrol the properties of the paper by the controlled addition ofadditives. More specifically, this embodiment considers the addition ofCO₂ in the wet end in a mixing chest. The measurement of the mostimportant variables in the inlet and outlet fiber flows such as ZetaPotential, charge demand, alkalinity, pH, etc. are taken in real-time,collected and made available to a data acquisition system. Themathematical relationship in the form of transfer function or any timedependent form are utilized to relate the CO₂ addition and the desiredwet end property, or controlled variable, such as Zeta Potential orcharge demand. In addition, similar relationships are utilized betweenpossible variations or disturbances in the inlet fiber flow and thecontrolled variable. Any feedback controller that tends to minimize thevariations between the desired controlled value and the real-timemeasurements in the outlet fiber flow is used.

[0171] In addition, the available real-time measurements from the inletfiber flow are used to design a predictive controller, such as feedforward controller, model predictive control (MPC), or any advancedcontroller. The feed forward controller modifies in a coordinated mannerthe output of the feedback controller. The feedback and feed forwardsignals are added and sent to a linear proportional control valve thatcontrols the CO₂ flow into the mixing tank.

[0172]FIG. 3 shows the performance of a feed forward control respondingto a normalized step change and a charge demand disturbance. It can beseen that the feedback controller can respond with no problems to theset point change, and that due to the feed forward controller, thedisturbance is rejected almost immediately, returning the plant to thedesired set point.

[0173] Illustrating another preferred embodiment, FIG. 4 shows a mixingchest 11, where a regulated inlet flow of CO₂ is supplied, 7. Someproperties of the fiber flow are measured on-line before going to themixing chest by measurements 12. At the same time, some on-lineproperties of the outlet fiber flow are measured by 13. All availableon-line measurements are used to compute the unobservable variables orstates, 14, using a real-time model, 15, and an observer or optimalestimator, such as Kalman Filter, 16.

[0174] The Kalman Filter observer is normally known as a model-basedobserver as it relies on the real-time model, 15. Data-driven observerssuch as neural networks, do not require a real-time model, but requirelarger amounts of data to be trained. The observer then estimates inreal-time the unobserved variables and passes this information to acontroller, 18, that manipulates the input of CO₂ that changes theunobserved variable to the desired set point.

[0175] This embodiment can be applied to control and optimization of thewet end of paper mills. It is intended to control the wet end inreal-time when the intended control variable is not measured oravailable in real-time. The available on-line measurements, 12 and 13,are related to control variables or states in what is called anobservation equation. The observation equation is part of the estimatoror observer 6. The observation equation can assume that there is somenoise in the instruments and that the rate of acquisition varies. Thisway, the information used by the estimator can also use off-lineinformation that is available in long time intervals.

[0176] The observation equation is related to the observer, as is thestate equation. The state equation is the transformation of the model,15, which is suitable for an estimation algorithm along with theobservation equation. The state equation also includes some modeluncertainty, which corresponds to the inaccuracies of the model. Thereare several estimation algorithms, but one of the most common is theKalman Filter (Kalman, R. E.) prediction for being an optimal estimator.The KF estimator is a real-time estimator that estimates theunobservable variables using the available measurements and theavailable model. The KF observer depends on the process model, 15, andso it is called a model-based observer.

[0177] If no model was available, a data-based observer such as neuralnetwork can be employed, but this requires a larger amount of data. Thereal-time optimal estimates, 14, become the process variablemeasurements required by the controller 18, which compares the estimateswith user-defined set points, and calculates a control output based onthe errors. The control output is sent to a linear proportional valvethat changes the addition of CO₂ into the reactor.

[0178] A method for controlling the CO₂ addition in a wet end processutilizing CO₂ addition is disclosed. A papermaking composition and CO₂are combined to create a CO₂-enriched papermaking composition. At leastone electrical property of either the papermaking composition or of theCO₂-enriched papermaking composition is either measured or estimated.The rate of addition of CO₂ to maintain the at least one electricalproperty within a pre-selected range of values is then controlled.

[0179] In one preferred embodiment, the electrical property is selectedfrom the group consisting of ZP, CD and ion concentration or anyequivalent thereto, and is estimated by measuring at least one propertyof either the papermaking composition or the CO₂-enriched papermakingcomposition selected from the group consisting of flowrate, CD, ZP, ionconcentration, Cy, pH, conductivity and alkalinity and using a model.Preferably, the ZP is estimated. Thus, the measured property can bemeasured from either the papermaking composition or the CO₂-enrichedpapermaking composition, and is preferably measured from the papermakingcomposition. Likewise, the estimated electrical property can beestimated for either the papermaking composition or the CO₂-enrichedpapermaking composition, and is preferably estimated for theCO₂-enriched papermaking composition.

[0180] In another preferred embodiment, a method for controlling the CO₂addition in a wet end process utilizing CO₂ addition includes moresophisticated controls. A papermaking composition and CO₂ are combinedto create a CO₂ -enriched papermaking composition. At least one propertyof the papermaking composition is measured or estimated and papermakingcomposition property data is generated. The papermaking compositionproperty data is provided to an advanced controller which generates apapermaking composition output component.

[0181] At least one property of the CO₂-enriched papermaking compositionis measured or estimated and CO₂-enriched papermaking compositionproperty data is generated. The CO₂-enriched papermaking compositionproperty data is provided to a feedback controller which generates anoutlet controller output component. The feedback controller iscompensated by analyzing the inlet controller output component and theoutlet controller output component. The inlet flow of CO₂ is controlledto maintain at least one property of the CO₂-enriched papermakingcomposition within a pre-selected range of values.

[0182] The at least one property of the papermaking composition ispreferably selected from the group consisting of flowrate, ZP, CD, ionconcentration, Cy, pH, conductivity and alkalinity. The at least oneproperty of the CO₂-enriched papermaking composition is preferablyselected from the group consisting of ZP, CD and ion concentration, andis most preferably ZP. Most prerably, the advanced controller comprisesa feed forward controller.

[0183] In alternatives of this embodiment, the advanced controllercomprises a feed forward controller, and the feed forward controlleruses either predictive control or inferential control.

[0184] In yet another preferred embodiment, a method for controlling theCO₂ addition in a wet end process utilizing CO₂ addition includessomewhat different controls. A papermaking composition and CO₂ arecombined to create a CO₂-enriched papermaking composition. On-linemeasurements of at least one property of the papermaking compositionselected from the group consisting of flowrate, ZP, CD, ionconcentration, Cy, pH, conductivity and alkalinity are made, papermakingcomposition property data is generated and transmitted to an observer.On-line measurements of at least one property of the CO₂-enrichedpapermaking composition selected from the group consisting of flowrate,ZP, CD, ion concentration, Cy, pH, conductivity and alkalinity are madeand CO₂-enriched papermaking composition data is generated. These dataare provided to an observer that generates at least one estimatedelectrical property of the CO₂-enriched papermaking composition selectedfrom the group consisting of ZP, CD and ion concentration. The observertransmits the papermaking composition property data, the CO₂—enrichedpapermaking composition property data and the estimated electricalproperty data to a controller, and the controller controlling the inletflow of CO₂ to maintain at least one electrical property of theCO₂-enriched papermaking composition within a pre-selected range ofvalues.

[0185] The observer can comprise a model, and can further refine theestimated electrical property data by analyzing inaccuracies presentedby the model and by analyzing expected errors in measurement. Thepapermaking composition property data, the CO₂-enriched papermakingcomposition property data and the estimated electrical property data canbe incorporated into a software sensor. The estimated electricalproperty data can be used to evaluate a set point and implement a realtime closed loop control.

[0186] Note that, in all of the embodiments described above, in a wetend process utilizing CO2 to control chemical properties in the wet endby injecting CO2 at specific locations in the process, the CO2 injectioncan be controlled to impart the desired properties either to the liquidor to the fibers, both of which can be present in the papermakingcomposition. These can be achieved using properties of the fibers or theliquid and rejecting process disturbances.

[0187] For example, the CO2 can be injected in at least one point of thewet end either directly to the fiber flow or to a fiber free liquid thatwill mix later on with the fibers. Alternatively, the CO2 can beinjected into a tank. The controlled injection can be either manual ifthe measurements are off-line or automatic if the measurements areon-line.

[0188] The manual control takes off-line samples and the properties aremeasured from these samples. The CO2 is then manually regulated based onsome recipes. The recipes for manual control are based on multivariablelinear or nonlinear regressions between the CO2 injection, themeasurements and the desired set points.

[0189] The automatic control can either be feedback, feedforward, acombination or an advanced controller. The feedback control takes atleast one measurement of the process after the mixing the fiber flow andthe CO2 rich flow (pure CO2 or water mixed with CO2). The feedforwardtakes at least one measurement of the process before the CO2 (pure CO2or water mixed with CO2) is injected and adjusts the CO2 before theprocess is affected. An advanced controller is either a combination ofthe feedforward and the feedback or an advanced controller such as butnot limited to cascade control, adaptive control, optimum control,robust control, neural network controller, fuzzy control, modelpredictive control, etc. The advanced controller adjusts the CO2 tomaintain the desired chemical property in the wet end, while rejectingany disturbance or minimizing the use of chemical additives in the wetend.

[0190] The chemical properties to be maintained by the CO2 controller inthe wet are but not limited to ZP (Zeta Potential), CD (Charge demand),pH, ion concentration, etc. The disturbances that can be rejected by theCO2 controller are but not limited to broke recirculation, variations ininlet charge demand, variations in inlet ZP, variations in pH,temperature, consistency, etc. The CO2 controller uses properties of theprocess that can be either intrinsic or extensive. Intrinsic informationcan be at least one but not restricted to pH, conductivity, CD, ZP, ionconcentration, etc. Extensive information can be at least but notrestricted to flow, volume, etc.

[0191] The on-line properties used by the controller can either bemeasured or unmeasurable. The measured properties can be at least onebut not limited to pH, conductivity, temperature, flow, CD, ZP, etc. Theunmeasurable or unobservable properties can be at least one but notlimited to CD, ZP, ion concentration, etc. The unmeasurable orunobservable properties can be estimated on-line and used by the CO2controller using an observer or estimator. The observer or estimator canpredict the unmeasurable or unobservable properties based on algorithmsprovided by, e.g., Kalman filters or neural networks. Observers useprocess knowledge either from fundamental models, empirical models orheuristic models.

[0192] Note further that, in the embodiments described above, ionconcentrations can be from [H+],[OH−],[Ca+2], [Na+], [HCO3−], [CO3−−],etc.

[0193] Moreover, in the embodiments described above, there are at leastthree techniques for performing automatic control: using properties inthe papermaking composition, using properties in the CO2-enrichedpapermaking composition, and using properties in both. For the firstcase, it is desired to use feed forward that can be typical feedforwardor inferential or predictive control. In the second case, a typicalfeedback becomes advanced when using adaptive, model predictive, robust,optimal, neural networks, fuzzy control, dynamic matrix control, etc.For the third case, combinations of both techniques can be employed.

[0194] While in the foregoing specification this invention has beendescribed in relation to certain preferred embodiments thereof, and manydetails have been set forth for purpose of illustration, it will beapparent to those skilled in the art that the invention is susceptibleto additional embodiments and that certain of the details describedherein can be varied considerably without departing from the basicprinciples of the invention.

We claim:
 1. In a wet end process utilizing CO₂ addition, a method forcontrolling the CO₂ addition comprising, in combination: combining apapermaking composition and CO2 to create a CO2-enriched papermakingcomposition; measuring or estimating at least one electrical property ofeither the papermaking composition or of the CO2-enriched papermakingcomposition; and controlling the rate of addition of CO2 to maintain theat least one electrical property within a preselected range of values.2. The method of claim 1, wherein the at least one electrical propertyis selected from the group consisting of ZP, CD and ion concentration.3. The method of claim 2, wherein the electrical property is estimatedby measuring at least one property of either the papermaking compositionor the CO₂ -enriched papermaking composition and estimating the ZP. 4.The method of claim 3, the electrical property being ZP.
 5. The methodof claim 3, the electrical property being CD.
 6. The method of claim 3,the electrical property being ion concentration.
 7. The method of claim3, wherein the at least one property is selected from the groupconsisting of flowrate, CD, ZP, ion concentration, Cy, pH, conductivityand alkalinity.
 8. The method of claim 4 wherein the at least oneproperty is selected from the group consisting of flowrate, CD, ionconcentration, Cy, pH, conductivity and alkalinity.
 9. The method ofclaim 5 wherein the at least one property is selected from the groupconsisting of flowrate, ZP, ion concentration, Cy, pH, conductivity andalkalinity.
 10. The method of claim 6 wherein the at least one propertyis selected from the group consisting of flowrate, CD, ZP, Cy, pH,conductivity and alkalinity.
 11. The method of claim 3, wherein the atleast one electrical property is estimated in the papermakingcomposition.
 12. The method of claim 3, wherein the at least oneelectrical property is measured in the CO₂-enriched papermakingcomposition.
 13. The method of claim 11, wherein the at least oneelectrical property is estimated in the papermaking composition.
 14. Themethod of claim 12, wherein the at least one electrical property isestimated in the papermaking composition.
 15. The method of claim 11,wherein the at least one electrical property is measured in theCO₂-enriched papermaking composition.
 16. The method of claim 12,wherein the at least one electrical property is measured in theCO₂-enriched papermaking composition.
 17. In a wet end process utilizingCO₂ addition, a method for controlling the CO₂ addition comprising, incombination: combining a papermaking composition and CO₂ to create aCO₂-enriched papermaking composition; measuring or estimating at leastone property of the papermaking composition and generating papermakingcomposition property data, and providing the papermaking compositionproperty data to an advanced controller constructed and arranged toreceive the papermaking composition property data and generate apapermaking composition output component; measuring or estimating atleast one property of the CO₂-enriched papermaking composition,generating CO₂-enriched papermaking composition property data andproviding the CO₂-enriched papermaking composition property data to afeedback controller constructed and arranged to receive the CO₂-enrichedpapermaking composition property data and generate an outlet controlleroutput component; compensating the feedback controller by analyzing theinlet controller output component and the outlet controller outputcomponent; and controlling the inlet flow of CO₂ to maintain at leastone property of the CO₂-enriched papermaking composition within apreselected range of values.
 18. The method of claim 17, wherein the atleast one property of the papermaking composition is selected from thegroup consisting of flowrate, ZP, CD, ion concentration, Cy, pH,conductivity and alkalinity.
 19. The method of claim 17, wherein the atleast one property of the CO₂-enriched papermaking composition isselected from the group consisting of ZP, CD and ion concentration. 20.The method of claim 18, wherein the at least one property of theCO₂-enriched papermaking composition is selected from the groupconsisting of ZP, CD and ion concentration.
 21. The method of claim 17,wherein the advanced controller comprises a feed forward controller. 22.The method of claim 21, wherein the at least one property of thepapermaking composition is selected from the group consisting offlowrate, ZP, CD, ion concentration, Cy, pH, conductivity and alkalinityand the at least one property of the CO₂-enriched papermakingcomposition is selected from the group consisting of ZP and CD.
 23. In awet end process utilizing CO₂ addition, a method for controlling the CO₂addition comprising, in combination: combining a papermaking compositionand CO₂ to create a CO₂-enriched papermaking composition; measuring orestimating at least one property of the papermaking composition selectedfrom the group consisting of flowrate, ZP, CD, Cy, pH, conductivity, ionconcentration and alkalinity, generating papermaking compositionproperty data and providing the papermaking composition property data toan advanced controller constructed and arranged to receive thepapermaking composition property data and generate an inlet controlleroutput component; measuring or estimating at least one property of theCO₂-enriched papermaking composition selected from the group consistingof ZP, CD and salt ion concentration and generating CO₂-enrichedpapermaking composition property data, providing the CO₂-enrichedpapermaking composition property data to a feedback controllerconstructed and arranged to receive the CO₂-enriched papermakingcomposition property data and generate an outlet controller outputcomponent; compensating the feedback controller by analyzing the inletcontroller output component and the outlet controller output component;and controlling the inlet flow of CO₂ to maintain at least one propertyof the CO₂-enriched papermaking composition within a preselected rangeof values.
 24. The method of claim 23, wherein the advanced controllercomprises a feed forward controller.
 25. The method of claim 24 whereinthe feed forward controller uses predictive control.
 26. The method ofclaim 24 wherein the feed forward controller uses inferential control.27. In a wet end process utilizing CO₂ addition, a method forcontrolling the CO₂ addition comprising, in combination: combining apapermaking composition and CO₂ to create a CO₂-enriched papermakingcomposition; on-line measuring at least one property of the papermakingcomposition selected from the group consisting of flowrate, ZP, CD, ionconcentration, Cy, pH, conductivity and alkalinity, generatingpapermaking composition property data and providing the papermakingcomposition property data to an observer; on-line measuring at least oneproperty of the CO₂-enriched papermaking composition selected from thegroup consisting of flowrate, ZP, CD, ion concentration, Cy, pH,conductivity and alkalinity, generating CO₂-enriched papermakingcomposition property data and providing the CO₂-enriched papermakingcomposition property data to the observer; the observer receiving thepapermaking composition property data and the CO₂-enriched papermakingcomposition property data and generating at least one estimatedelectrical property of the CO₂-enriched papermaking composition selectedfrom the group consisting of ZP, CD and ion concentration, the observergenerating estimated electrical property data for the at least oneelectrical property and transmitting the papermaking compositionproperty data, the CO₂-enriched papermaking composition property dataand the estimated electrical property data to a controller; and thecontroller controlling the inlet flow of CO₂ to maintain at least oneelectrical property of the CO₂-enriched papermaking composition within apreselected range of values.
 28. The method of claim 27, the observercomprising a model.
 29. The method of claim 27, the papermakingcomposition property data, the CO₂-enriched papermaking compositionproperty data and the estimated electrical property data beingincorporated into a software sensor.
 30. The method of claim 28, thepapermaking, composition property data, the CO₂-enriched papermakingcomposition property data and the estimated electrical property databeing incorporated into a software sensor.
 31. The method of claim 28,the observer further refining the estimated electrical property data byanalyzing inaccuracies presented by the model.
 32. The method of claim28, the observer further refining the estimated electrical property databy analyzing expected errors in measurement.
 33. The method of claim 28,the observer further refining the estimated electrical property data byanalyzing inaccuracies presented by the model and by analyzing expectederrors in measurement.
 34. The method of claim 30, the observer furtherrefining the estimated electrical property data by analyzinginaccuracies presented by the model.
 35. The method of claim 30, theobserver further refining the estimated electrical property data byanalyzing expected errors in measurement.
 36. The method of claim 30,the observer further refining the estimated electrical property data byanalyzing inaccuracies presented by the model and by analyzing expectederrors in measurement.
 37. The method of claim 28 further comprisingusing the estimated electrical property data to evaluate a set point andimplement a real time closed loop control.
 38. The method of claim 30further comprising using the estimated electrical property data toevaluate a set point and implement a real time closed loop control. 39.The method of claim 36 further comprising using the estimated electricalproperty data to evaluate a set point and implement a real time closedloop control.
 40. In a wet end process utilizing CO addition, a methodfor controlling the CO₂ addition comprising, in combination: combining apapermaking composition and CO₂ to create a CO₂-enriched papermakingcomposition; on-line measuring at least one property of the papermakingcomposition selected from the group consisting of flowrate, ZP, CD, ionconcentration, Cy, pH, conductivity and alkalinity, generatingpapermaking composition property data and providing the papermakingcomposition property data to an observer; on-line measuring at least oneproperty of the CO₂-enriched papermaking composition selected from thegroup consisting of flowrate, ZP, CD, ion concentration, Cy, pH,conductivity and alkalinity, generating CO₂-enriched papermakingcomposition property data and providing the CO₂-enriched papermakingcomposition property data to the observer; the observer receiving thepapermaking composition property data and the CO₂-enriched papermakingcomposition property data and using a model to generate at least oneestimated electrical property of the CO₂-enriched papermakingcomposition selected from the group consisting of ZP, CD and ionconcentration; the observer refining the estimate for the at least oneelectrical property by analyzing inaccuracies presented by the model andby analyzing expected errors in measurement; the observer transmittingthe papermaking composition property data, the CO₂-enriched papermakingcomposition property data and the refined estimated electrical propertydata to a controller; and the controller controlling the inlet flow ofCO₂ to maintain at least one electrical property of the CO₂-enrichedpapermaking composition within a preselected range of values.